{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "4507a467",
   "metadata": {},
   "source": [
    "**<font size=4 color=#BB3D00 face=微软雅黑>在下采样前进行滤波</font>**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "03a2bf97",
   "metadata": {},
   "source": [
    "<font size=3  face=微软雅黑>**※Matlab案例**</font> "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "758cf566",
   "metadata": {},
   "source": [
    "网址：https://ww2.mathworks.cn/help/signal/ug/filtering-before-downsampling.html \n",
    "描述：本案例由1个示例构成：   \n",
    "- <font color=DarkOrChid>示例1：如何在下采样前进行滤波以减轻混叠造成的失真</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e22ae0ba",
   "metadata": {},
   "source": [
    "<font size=3 face=微软雅黑>**※Python案例**</font> "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3446294e",
   "metadata": {},
   "source": [
    "针对以上案例，采用Python语言实现。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b0055522",
   "metadata": {},
   "source": [
    "- <font color=DarkOrChid>示例1：如何在下采样前进行滤波以减轻混叠造成的失真</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7c9768b4",
   "metadata": {},
   "source": [
    "此示例说明如何在下采样前进行滤波以减轻混叠造成的失真。您可以使用 decimate 或 resample 以通过一个函数进行滤波和下采样。您也可以先对数据进行低通滤波，然后使用 downsample。创建基带频谱支持大于 π 弧度的信号。使用 decimate 以在下采样之前通过 10 阶 Chebyshev I 类低通滤波器对信号滤波。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5cec01a5",
   "metadata": {},
   "source": [
    "创建信号并绘制幅值频谱。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "d528e599",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy import signal\n",
    "from scipy import *\n",
    "\n",
    "f = [0,0.2500,0.5000,0.7500,1.0000]\n",
    "a = [1.00,0.6667,0.3333,0,0]\n",
    "nf=512\n",
    "b1=signal.firwin2(nf-1, f,a, nfreqs=None, window='hamming', nyq=None, antisymmetric=False, fs=None)\n",
    "[h1,h2]=fft.fftshift(signal.freqz(b1, 1, nf, whole=True, plot=None, fs=2*np.pi, include_nyquist=False))\n",
    "omg=np.linspace(-np.pi,np.pi-2*np.pi/nf,nf)\n",
    "fig = plt.figure(dpi=100,figsize=(8,6))\n",
    "ax1 = fig.add_subplot(111)\n",
    "ax1.plot(omg/np.pi,abs(h1))\n",
    "plt.xlabel('$\\pi$ rad/sample')\n",
    "plt.ylabel('Magnitude')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "86153fba",
   "metadata": {},
   "source": [
    "使用 10 阶 Chebyshev I 类低通滤波器对信号进行滤波，然后以 2 为因子下采样。绘制原始信号以及经过滤波和下采样的信号的幅值频谱。低通滤波器减少了区间 [−π/2,π/2] 之外的混叠失真量。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "97b87c53",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "y = signal.decimate(b1,2,10)\n",
    "[h3,h4]=fft.fftshift(signal.freqz(y, 1, nf, whole=True, plot=None, fs=2*np.pi, include_nyquist=False))\n",
    "fig = plt.figure(dpi=100,figsize=(8,6))\n",
    "ax1 = fig.add_subplot(111)\n",
    "ax1.plot(omg/np.pi,abs(h1),label='Original')\n",
    "ax1.plot(omg/np.pi,abs(h3),label='Downsampled')\n",
    "plt.xlabel('$\\pi$ rad/sample')\n",
    "plt.ylabel('Magnitude')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
